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The aim of this article is to study the relationships and models among the Van den Dool and Kratz equation, the gas chromatography (GC), and the Bézier curves constructed by aid of the Bernstein polynomials. Another aim of this article is to introduce open problems that contribute to real‐world problems involving mathematics, chemistry, and plant biology, including the Van den Dool and Kratz equation, the GC, and Bézier curves. Searching for the solutions of these problems may have qualities that will create the potential that can enter the field of study of many researchers. As a result of these goals, the usability of Bézier curves was investigated while determining the chemical composition of essential oil obtained from Potentilla aladaghensis Leblebici, by applying the retention index from the Van den Dool and Kratz equation and evaluating chemical compositions of the essential oil are characterized by GC–mass spectrometry (GC–MS). The Van den Dool and Kratz equation results have the potential to be used not only in the chemical compositions of the oils but also in applied mathematics and other fields. Moreover, we construct a new special finite sum. A lower bound and inequality are also given for the finite special sum involving the dead time associated with the isocratic step. Some applications and criticisms are given that include this lower bound and inequality for these sums and its effects on the chemical compositions of essential oil and the Van den Dool and Kratz equation.

In this work, chemical composition and antimicrobial activity of the essential oils of Galium incanum, Galium dieckii ve Galium aladaghense were firstly reported. The essential oils were obtained from the all parts of the plant by hydrodistillation and analyzed by using GC-MS. Antimicrobial activity of synthezied essential oils was carried out against 5 pathogen bacteria Escherichia coli (E. coli) ATCC 25922, Staphylococcus aureus (S. aureus) ATCC 25923, Pseudomonas syringae pv. tomato (P. syringae) DC300, Salmonella enterica serotype Typhmurium (S. typhmurium) SL 1344 and Streptococcus mutans (S. mutans) ATCC 25175. According to the results, it was determined that isolated essential oils comprised of 61 compounds. Compounds of essential oils included that structure monoterpene (8.2%), monoterpenoid (14.75%) and sesquiterpene (14.75%). Unclassified compounds have been identified as other compounds. From the antimicrobial activity was observed that the isolated essential oil from Galium incanum, Galium dieckii ve Galium aladaghense exhibited a potent inhibitory effect against all gram negative and gram positive bacteria with diameter of inhibition zones ranging from 4.3 to 12.3 mm. Essential oil of Galium aladaghense indicated that high antimicrobial activity on all bacteria than Galium incanum and Galium dieckii.

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The Hamit pluton forms part of the Central Anatolian Crystalline Complex. It is located N-NE of Kaman (Kirsehir). It covers an area of about 120 km 2. The geochemical contents of 63 rock samples collected from this pluton were analyzed for their origin, homogeneity and relationship with crustal rocks. Their element contents were determined by using X-Ray Fluorescence spectroscopy. The samples were divided into 2 major groups based on their similarities: Group 1 contained 63.5% of the samples and indicated they were formed from melts whose contents might have evolved greatly due to crustal assimilation; while the 36.5% of samples belonged to Group 2, and show minimal evolution of the melt. According to the variation in K/Rb ratio versus SiO 2 and the Rb/Zr versus SiO 2 the initial melt had experience great evolution due to crustal assimilation. The initial melt is considered to have contained "most" of SiO